Civil Engineering Reference
In-Depth Information
6.1.2.4
Constitutive laws of materials
The softening concrete stress-strain curve proposed by Hsu (1993, 1994) is
adopted here. General expressions for the constitutive laws of concrete and
steel for a multicell box are as follows:
Concrete struts:
σ
=
k
ζ
f
(6.10)
′
di
1
i
i c
k
i
= ξ ε
(
,
ζ
)
(6.11)
1
1
dsi
i
ζ
=
ξ
2
(
ε
,
ε
)
(6.12)
i
di
ri
Steel:
f
li
= ξ ε
3
(
)
(6.13)
li
f
ti
= ξ ε
4
(
)
(6.14)
ti
Combining governing equations for compatibility condition based on the
unified theory (Hsu 1993) with selected constitutive equations, in this case,
the softening concrete stress-strain curve, solution can be derived. For
details of the solution of a single cell, refer to Hsu (1993, 1994), Fu and
Yang (1996), and Fu and Tang (2001).
6.1.3 Construction geometry control
Curved bridges can be built segmentally or nonsegmentally where seg-
mental bridges may adopt precast or cast-in-place construction of bridge
members. The short-line match-cast joint method of precasting concrete
segments has proved to be the most versatile and reliable way of build-
ing precast segmental bridges. The geometry control of segments casting
in yard is a unique issue of precast segmental bridges, and its application
is critical to reproduce the designed bridge curves after assembling. This
long-standing topic is always a part of the design and construction of seg-
mental bridges, especially for curved segmental bridges. More details about
this topic will be discussed in Section 18.6.
6.2 PrinCiPle and Modeling of Curved
ConCrete Bridges
A variety of modeling approaches can be applied when analyzing hori-
zontal curved bridges. Among these methods, plane frame analysis, spine
beam analysis, and 3D FEM are the most popular methods that are used
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